A Contour-Integral Based Method for Counting the Eigenvalues Inside a Region
- 82 Downloads
In many applications, the information about the number of eigenvalues inside a given region is required. In this work, we develop a contour-integral based method for this purpose. Our method is motivated by two findings. There exist methods for estimating the number of eigenvalues inside a region in the complex plane, but our method is able to compute the number exactly. Our method has a good potential to be implemented on a high-performance parallel architecture. Numerical experiments are reported to show the viability of our method.
KeywordsEigenvalue Generalized eigenvalue problem Contour integral Spectral projection
Mathematics Subject Classification15A18 58C40 65F15
I would like to thank Professor Raymond H. Chan, my thesis advisor, for his help in preparing this paper. I also would like to thank the anonymous reviewers for their useful suggestions which have greatly improved this paper. This work was supported by the National Natural Science Foundation of China (NSFC) under Grant 11701593.
- 4.Boisvert, R.F., Pozo, R., Remington, K., Barrett, R., Dongarra, J.: The matrix market: a web resource for test matrix collections. In: Boisvert, R.F. (ed.) Quality of Numerical Software: Assessment and Enhancement, IFIP Advances in Information and Communication Technology, pp. 125–137. Chapman & Hall, London (1997)CrossRefGoogle Scholar
- 9.Di Napoli, E., Polizzi, E., Saad, Y.: Efficient estimation of eigenvalue counts in an interval. arXiv:1308.4275
- 16.Kamgnia, E.R., Philippe, B.: Counting eigenvalues in domains of the complex field. arXiv:1110.4797
- 17.Lin, L., Saad, Y., Yang, C.: Approximating spectral densities of large matrices. arXiv:1308.5467